What you are looking at in your photo is an elbow, not a bracket and poking out of the bottom is blue MDPE water pipe.
It is used often to bring mains water into houses from the water company main.
The "layflat" pipe you refer to is used inside properties instead of copper pipe.
The difference is that the blue and sometimes black pipe is designed for rugged external and underground use whereas the layflat is not.
It might work if it was laid in ducting.
I would just use the blue pipe.
BTW, the term layflat is also used for flexible hose that can be rolled up and is flat with no water in it.
The elbow is a compression type and one brand is Philmac.
It isn't good practice to have an unsupported pipe coming straight out of the wall, nor is it good to have it unprotected from frost, though that depends where you live.
To answer your question, I know that Philmac do fittings to join MDPE pipe to just about anything else.
If you use the layflat pipe, you need to ask the manufacturer (e.g. John Guest Speedfit) if their fittings are suitable for external use.
Remember that all metric pipe is measured on the external diameter.
One tip. Protect the joints with tape or even a plastic bag to keep grit out.
There is a delicate "O" ring seal and sometimes you won't be able to get the fitting apart if it gets crud in it.
Another tip, don't use a hacksaw to cut either type of pipe. Use the proper pipe cutter.
The jagged hacksaw cut can ruin the fitting seal.
You might get away with using layflat, but I wouldn't recommend it.
You can use either type of pipe with conventional brass compression fittings, but you need to use an insert in the pipe to take the force of the fitting when tightened.